Molecular Dynamics Simulation Study on CO2 Physical Absorption

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Molecular Dynamics Simulation Study on CO2 Physical Absorption Mechanisms for Ethylene-Glycol-Based Solvents Using Free Energy Calculations Ryo Nagumo,*,† Yukihiro Muraki,† Shuichi Iwata,† Hideki Mori,† Hiromitsu Takaba,‡ and Hidetaka Yamada§ †

Department of Materials Science and Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan Department of Environmental Chemistry and Chemical Engineering, Kogakuin University 2665-1 Nakano-machi, Hachioji-shi, Tokyo 192-0015, Japan § Research Institute of Innovative Technology for the Earth (RITE), 9-2 Kizugawadai, Kizugawa-shi, Kyoto 619-0292, Japan ‡

S Supporting Information *

ABSTRACT: Molecular mechanisms of CO2 physical absorption are significant for the development of higher-performance CO2 absorbents. In this study, the free energy profiles for CO2 approaching several types of ethylene glycol (EG)-based solvent molecules and their derivatives (diols, ethers, and alkanes, etc.) were evaluated using molecular dynamics simulations. A desolvation barrier appeared in the free energy profiles in the pure component solvent, corroborating the negative contribution of a void effect on CO2 affinities. The profiles in vacuum were also estimated to investigate the functional group effects in a constituent solvent molecule. The profiles for the EG-based solvent molecules showed similar minimum values to their derivative diols, while the values for their derivative ethers and alkanes were markedly higher. CO2 solubility is certainly determined by two major factors: the specific CO2 affinities of the constituent hydroxyl groups and a steric void effect near an absorbed CO2 molecule.

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INTRODUCTION CO2 capture is a topic of major research and development interest due to its role in greenhouse gas mitigation.1 Gas absorption is a promising CO2 separation process.2,3 At present, the most widely used solvents for CO2 absorption are amine solutions,4−9 mainly because they can strongly absorb CO2 by chemical reactions to form carbamates even at ambient pressures. To achieve higher CO2 solubilities, alternative amine absorbents were recently proposed that allow more energy-effective and lower-cost regeneration.10,11 At higher CO2 pressures (>1 MPa), physical absorption is also promising because the solvent regeneration process can be simplified to be less energy-intensive.12,13 One of the most well-known physical absorbents is Selexol, a commercial poly(ethylene glycol) dimethyl ether (PEGDME)-based solvent.14 Ionic liquids, which include both chemical and physical absorbents for CO2 capture, are also considered to be potential absorbents due to their extremely low vapor pressures.15−17 Commercially available solvents such as polyethylene glycol (PEG), PEGDME, tetraglyme, and glycerol have been used for physical absorption because of their low vapor pressures, high stabilities, and nontoxicities.18,19 Previous studies have reported experimental data on CO2 solubilities at ambient pressures and temperatures, as listed in Table 1. This table shows very © XXXX American Chemical Society

Table 1. Previous Experimental Data of Absorbed CO2 Amounts absorbed amounta [mmol mol−1] absorbent

absorbed amount [g L−1] 298 K18,b

298 K18,b

303 K19,c

15.1 15.1

61 92

10 14 23 33

6.9 4.9 17.2

22 24 29

PEG150 PEG200 PEG300 PEG400 PEGDME150d tetraglyme glycerol

a Converted from the literature data.18,19 bMeasured at atmospheric pressure. cMeasured at pressures over a range from 137.7 to 148.3 kPa. d Also identified as DEGDME in this work.

Received: March 18, 2016 Revised: June 14, 2016 Accepted: July 5, 2016

A

DOI: 10.1021/acs.iecr.6b01074 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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correlated with the intermolecular affinities between a CO2 molecule and a solvent molecule.20 Thus, we also discuss the correlation between the predicted profiles and the CO2 solubilities in mmol mol−1. These thermodynamic evaluations provide insight into the CO2 physical absorption behaviors at the atomistic levels.

different CO2 solubility values for PEG200 and PEG300, mainly because the approaches used to measure these solubilities were different (as described in our previous study).20 The table also suggests that solvents with hydroxyl groups show higher CO2 solubilities in g L−1; i.e., solubilities increase in the following order: tetraglyme < PEGDME150 < PEG200 = PEG300 < glycerol. In contrast, when measured in mmol mol−1, which directly indicates the number of solvent molecules required to absorb one CO2 molecule, solubilities increase in the order of PEGDME150 ∼ tetraglyme ∼ glycerol < PEG200 < PEG300. Intriguingly, CO2 solubility in PEG300 is much larger than that for PEG200 when measured in mmol mol−1, whereas the solubilities in g L−1 are almost equal. The orders of CO2 solubilities listed in Table 1 indicate that, beside the hydroxyl group, the solvent chain length is a critical factor for enhancing the CO2−solvent molecular interaction. In the case of PEG solvents, CO2 solubilities in mmol mol−1 increase when the chain length of the ethylene glycol repeating units is longer, meaning that the number of PEG solvent molecules required to absorb one CO2 molecule decreases with an increase in the chain length. Table 1 also shows that a larger number of glycerol molecules than PEG200 and PEG300 molecules are required for the absorption of one CO2 molecule. In terms of CO2 absorption mechanisms at the atomistic levels, the polarity of the intramolecular carbon−oxygen bonds in CO2 molecules certainly leads to interactions with both the polar hydroxyl groups and the ether bonds of the surrounding solvent molecules, as shown in Figure 1.21−23 The Lewis acid−

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SIMULATION METHODS The chemical structures of EG2, EG3, EG4, DEGDME, and their derivatives are shown in Figure 2 and those of glycerol and

Figure 2. Chemical structures of ethylene-glycol-based solvent molecules: (a) EG2 and derivatives, (b) EG3 and derivatives, (c) EG4 and derivatives, and (d) DEGDME and derivatives. Figure 1. Schematic illustration of polar interactions between a CO2 molecule and a functional group of surrounding ethylene-glycol-based solvent molecules: (a) terminal hydroxyl group and (b) ether bond.

base reaction between the acidic CO2 and the electron-rich oxygen atoms of the PEG molecules is likely responsible for the enhanced CO2 solubilities. It should be noted that the polarity of the hydroxyl group is stronger than that of the ether bond. However, the molar ratio of the ether bonds to the hydroxyl group in a PEG molecule increases with an increase in the chain length. These facts make it difficult to understand the CO2− solvent interaction comprehensively at the atomistic level. In considering the intermolecular affinities between a CO2 molecule and a solvent molecule, it remains unclear how the hydroxyl groups and/or ether bonds contribute to the enhancement of the CO2 solubilities. Possibly there are other significant factors for determining CO2 solubilities. In this study, we investigate the effects of the constituent groups of solvent molecules and some steric effect in the vicinity of the CO2 molecule on CO2 affinities. We evaluated the free energy profiles for CO2 approaching several types of solvent molecules and their derivatives: ethylene glycol monomer (EG1), dimer (EG2), trimer (EG3), and tetramer (EG4); diethylene glycol dimethyl ether (DEGDME); glycerol; and their derivatives such as diols, ethers, and alkanes. Although it should be noted that commercial PEG and PEGDME solvents consist of a mixture of solvent molecules containing different numbers of repeat units, which makes it difficult to achieve highly accurate estimates of CO2 solubilities, the free energies can be directly

Figure 3. Chemical structures of six solvent molecules: glycerol and derivatives.

its derivatives in Figure 3. The derivative diol, ether, and alkane molecules are denoted as EG2-diol, EG2-ether, and EG2alkane, respectively. To discuss the effect of the ethylene glycol chain length on CO2 affinity, we evaluated the free energy profiles of a CO2 molecule approaching a solvent molecule in single-component EG1, EG2, EG3, EG4, DEGDME, and glycerol solvents. All simulations were performed using our inhouse molecular dynamics (MD) program. A schematic of a CO2 molecule approaching one EG2 molecule in the surrounding EG2 solvent molecules is illustrated in Figure 4. The free energy profiles for a CO2 molecule approaching several types of solvent molecules (EG2, EG3, EG4, DEGDME, and glycerol) and their derivatives were also estimated for simulation cells containing no molecules other than a pair of a B

DOI: 10.1021/acs.iecr.6b01074 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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surrounding solvent molecules are denoted as ”vacuum systems”. We evaluated the free energy profiles by using the potential of mean force (PMF).24 The PMF was calculated from the sum of the differences in the Helmholtz energy, similar to our previous studies.25−27 For the potential parameters, the default values of the consistent valence force field (CVFF)28 were used with the exception of the parameters used for the CO2 molecule. The bond stretching and angle bending parameters for the CO2 molecule are not included in the original CVFF, and so the parameters for the CO2 molecule used in this study are based on those used by Nieto-Draghi and co-workers.29 The potential parameters were the same as those in our previous study,20 where the experimental CO2 solubilities and the simulated minimum values of the free energy profiles showed good correlations. Nonbonding interactions were described with a 12-6 Lennard−Jones potential, which was truncated at 1.0 nm. Long-range electrostatic interactions were

Figure 4. Schematic diagram of a CO2 molecule approaching an ethylene glycol dimer. For clarity, the surrounding solvent molecules are omitted.

CO2 molecule and a solvent molecule. By considering these simplified models, we aim to investigate the inherent effects of the constituent functional groups of the solvents on their CO2 affinities. In this study, the models where the surrounding solvent molecules are included in the simulation cell are denoted as ”solvent systems”, and those without the

Figure 5. Free energy profiles at 298 K for CO2 approaching six types of solvent molecules in pure component solvents: (a) glycerol, (b) EG1, (c) EG2, (d) DEGDME, (e) EG3, and (f) EG4. C

DOI: 10.1021/acs.iecr.6b01074 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research treated with the particle mesh Ewald method.30 In solvent systems where the surrounding solvent molecules were included, the initial simulation system was a 10.0 × 10.0 × 10.0 nm3 cubic box containing a CO2 molecule and one solvent molecule pair and the surrounding solvent molecules. An MD simulation was performed to compress the box artificially (isobaric conditions are not imposed) at 298 K with a time step of less than 1 fs to avoid the overlapping between neighboring atoms, and the simulation was terminated after checking that the density of the simulation cell was in good agreement with the experimental data18 at ambient temperature and pressure. After the compressed cubic box was obtained, another MD simulation was performed in the canonical ensemble (constant number of atoms, volume, and temperature in the simulation box) for data sampling. The system was maintained at 298 K using a scaling method, and the initial velocities of the molecules in the boxes were set corresponding to the Boltzmann distribution. In all these simulations for data sampling, time steps for each MD step were set to 1 fs. In vacuum systems, only a single CO2 molecule/solvent molecule pair was placed in a fixed 8.0 × 8.0 × 8.0 nm3 cell, and the MD simulation started in the canonical ensemble for data sampling without considering the compression processes, although the other simulation conditions were similar to those for the solvent models. In all our simulations, a periodic boundary condition was applied in all three directions. Computational periods for the data sampling are given in Table S1 for the solvent systems and in Table S2 for the vacuum systems. Table S1 also provides the numbers of solvent molecules around a CO2 molecule/molecule pair in the simulation cells and cubic cell lengths for data sampling. Considering cell size effects and computational costs, our cell lengths were between 2.5 and 2.8 nm. In vacuum systems, it was necessary to set time steps of less than 1 fs, mostly for ether and alkane derivative solvents, likely because the time scales of conformational changes for these solvent molecules were smaller than those for the other absorbents. Although the absolute computational times are reduced proportionally to the time steps for each MD step, the data sampling sufficiency for free energy calculations can be confirmed by checking whether the fluctuations of the free energy profiles on the simulation times are insignificant, as described in the following sections.

characteristic barriers arise due to the contribution from the void between the two approaching molecules, where other solvent molecules rarely exist, resulting in a decrease in the entropy of the surrounding solvent and an accompanying increase in free energy. At further intermolecular distances, surrounding solvent molecules can pass between the CO2 and the corresponding solvent molecule. In contrast to Figure 5a−c, the heights of the desolvation barriers seem close to zero in Figure 5d−f. This is because the EG3 and EG4 molecules cannot pass through the void, even at longer intermolecular distance (∼1.0 nm) due to longer chains. It should be noted that more accurate assessments of the minimum values in free energy profiles are not necessarily required to see if the void effect between two approaching molecules is significant. In Figure 5, the heights of the desolvation barriers in the free energy profiles for the overall computational period decrease in the order of glycerol (1.5 kJ mol−1) > EG1 (1.2 kJ mol−1) > EG2 (0.77 kJ mol−1) > DEGDME (0.47 kJ mol−1) > EG3 (0.36 kJ mol−1) > EG4 (0.17 kJ mol−1). With the exception of the profile of a glycerol molecule, which has a different type of molecular structure from the other five EG-based solvent molecules, the height decreases with an increase in molecular length, strongly suggesting a significant contribution of the steric void to the difference in energetic barrier. A lower free energy barrier generally enhances the CO2 affinity. Thus, the order of the heights of the desolvation barriers certainly corroborates the CO2 solubility data in mmol mol−1 for the EGbased solvents shown in Table 1: the longer the chain of a solvent molecule, the higher its CO2 affinity. Figure 5 indicates that the desolvation barrier due to steric effects is a significant factor for CO2 solubilities in EG-based physical solvents. Although we had anticipated in advance that such barriers would not appear in the free energy profile, contributions of the surrounding solvent molecules to the affinities between a CO2 molecule and a solvent molecule are certainly much larger than we expected. To exclude the interactions between the surrounding solvent molecules and to evaluate the inherent intermolecular affinities between a CO2 molecule and one solvent molecule, we calculated free energies for a CO2 molecule approaching a solvent molecule in vacuum. The details are provided in the following sections. CO2 Affinities in Vacuum. Figure 6 shows the predicted free energy profiles for a CO2 molecule approaching EG2, EG3, EG4, DEGDME, and their derivatives (diols, ethers, alkanes, etc.) in vacuum. The profiles for EG3, EG4, and DEGDME were taken from those in our previous study.20 Although the profile for EG2 was also reported there, we conducted new free energy calculations with the same procedure and confirmed that a very similar free energy profile was obtained. It should be noted that the data samplings for the free energy calculations in this figure are certainly sufficient, regardless of the setting values of the time steps listed in Table S2, because fluctuations of the free energy profiles on the simulation times are insignificant (shown in Figures S1, S2, S3, and S4 for the EG2, EG3, EG4, and DEGDME solvents and their derivatives, respectively). As shown in Figure 6a−c, the profiles for EG2, EG3, and EG4 solvent molecules show similar minimum values to those of their respective derivative diols, and these values were remarkably smaller than those of ethers and n-alkanes. The minimum values for the EG and diol molecules ranged from −5.3 to −2.5 kJ mol−1, while those for the ethers and diols were higher than −1.2 kJ mol−1. In the profiles for DEGDME and the derivatives in Figure 6d, the shapes of the free energy

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RESULTS AND DISCUSSION CO2 Affinities in Solvent Molecules. The predicted free energy profiles for a CO2 molecule approaching a solvent molecule (glycerol, EG1, EG2, DEGDME, EG3, and EG4) in the solvent models are shown in Figure 5a−f, respectively. The horizontal axes represent the distance between the centers of mass of the approaching CO2 and solvent molecule. This figure includes the individual profiles obtained by dividing the overall computational period for data sampling into three equal time intervals. In Figure 5a,b,d, the fluctuations of the profiles of the CO2 molecule seem insignificant. In contrast, in Figure 5c,e,f, the profiles fluctuate around the energetically stable points, within a range of ca. 1 kJ mol−1, indicating that more sufficient data samplings should be taken to more accurately observe the free energy profiles. However, the fluctuations are less significant in some areas, particularly around the desolvation barriers. Figure 5a,b clearly exhibit the usual features of PMF curves: a contact minimum and a desolvation barrier.31 This barrier also appears at an intermolecular distance of ca. 0.7 nm in Figure 5c. As mentioned in our previous study,25 these D

DOI: 10.1021/acs.iecr.6b01074 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 7. Snapshots of CO2 approaching a solvent molecule at 107 MD steps in a vacuum: (a) EG2, (b) EG2-diol, (c) EG2-ether, (d) EG2-alkane, (e) EG3, (f) EG3-diol, (g) EG3-ether, (h) EG3-alkane, (i) EG4, (j) EG4-diol, (k) EG4-ether, (l) EG4-alkane, (m) DEGDME, (n) DEGDME-methoxy, (o) DEGDME-ether, and (p) DEGDMEalkane; the temperature was set at 298 K.

Figure 6. Free energy profiles at 298 K for CO2 approaching four types of solvent molecules and their respective derivatives in vacuum: (a) EG2 and derivatives, (b) EG3 and derivatives, (c) EG4 and derivatives, and (d) DEGDME and derivatives.

profiles are comparable, and the minimum values are higher than −1.0 kJ mol−1, indicating that methoxy, ether, and alkyl groups have similar CO2 affinities. Figure 6 confirms that the minimum values of the EG solvent molecules and their derivative diols are substantially smaller than those for their derivative ethers and alkanes. This indicates that the hydroxyl group promotes CO2 affinity more strongly than the ether bonds or methoxy groups, and that ether bonds alone do not entirely contribute to the enhancement of the affinities. It is possible that the differences in the minimum values in Figure 6 are due to the energetic stabilization derived from the steric enclosure of molecular chains of the solvents. To check the conformation, we observed terminal snapshots from the MD simulations for data sampling of the 12 CO2 molecule/ solvent molecule pairs shown in Figure 6. The snapshots are shown in Figure 7, where the intermolecular distance was fixed at the minimum points in the free energy profiles. Although the averaged conformations over the entire simulation times were not evaluated, this figure certainly suggests that EG2, EG3, EG4, and their derivative diols are more likely to encircle a CO2 molecule than the other derivatives. Thus, an absorbed CO2 molecule is possibly stabilized by solvent encirclement due to the polar effect of hydroxyl groups and the size effect of the solvent molecules. Glycerol has a different type of molecular structure than the EG-based molecules, and there is no possibility of a glycerol molecule encircling a CO2 molecule sterically (as EG-based solvent molecules and their derivatives can do). Therefore, free energy calculations for a glycerol molecule and derivatives enabled us to exclude the energetic effects of steric enclosure by molecular chains. Figure 8 shows the estimated profiles of a CO2 molecule approaching a glycerol molecule and five types of derivative solvent molecules (1,2-butanediol, 2-methylpropane-1,3-diol, 2-methylbutanol, 3-pentanol, and 3-methylpentane). As shown in Figure S5, we obtained three individual

Figure 8. Free energy profiles at 298 K for CO2 approaching a glycerol molecule and its derivatives in vacuum. The profile for glycerol was taken from our previous study.20

profiles and almost no fluctuations over the elapsed time, demonstrating that the data samplings in the free energy calculations are sufficient. In Figure 8, the minimum value of the profile for 3-methylpentane (ca. −0.83 kJ mol−1), which has no hydroxyl groups, is remarkably larger than those for a glycerol molecule and the other derivatives (−2.4 to −1.9 kJ mol−1). This corroborates that the presence of a hydroxyl group in a solvent molecule is a key factor of CO2 affinity, and that CO2 affinities are nearly independent of how many hydroxyl groups are in the molecular structure of each solvent molecule. Figure 9 shows the terminal snapshots from MD simulations for data sampling for the six types of CO2 molecule and solvent molecule pairs in Figure 8. Here, the intermolecular distance was fixed at the minimum point in each free energy profile. As we expected, none of the five types of derivative solvents, nor the glycerol molecule, encircled a CO2 molecule. These snapshots confirm that the effects of steric enclosure of molecular chains on CO2 affinities were successfully excluded, reinforcing our speculation that CO2 molecules are more dominantly attracted by hydroxyl groups than by ether bonds, methoxy groups, and alkyl groups. In future investigations, specification of the time-averaged snapshots will contribute to the highly accurate quantification of the stabilization effects by solvent encirclement. E

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the glycerol molecule, which has a different molecular structure from that of the other solvent molecules. The order certainly corroborates the significant contribution of the steric void effect to the decrease in CO2 affinity, particularly for the solvent molecules with shorter chains. We also evaluated the free energy profiles for a CO2 molecule approaching several types of solvent molecules (EG2, EG3, EG4, DEGDME, and glycerol) and their derivatives (diols, ethers, alkanes, etc.) in vacuum. The profiles for EG2, EG3, and EG4 solvent molecules show similar minimum values to their derivative diols, and the values are remarkably smaller than those for ethers and alkanes. In the free energy profiles for DEGDME and its derivatives, the profiles have comparable shapes, indicating that methoxy groups, ether bonds, and alkyl groups have similar CO2 affinities. To check the molecular conformations, terminal snapshots from the MD simulations were observed for the CO2 molecule/solvent molecule pair. The snapshots corroborate the idea that solvent molecules with longer chains such as EG3 and EG4 are more likely to encircle a CO2 molecule, certainly resulting in an energetic stabilization. The investigations for a glycerol molecule and its derivatives in vacuum enabled us to exclude this steric stabilization effect and to evaluate the inherent contribution of the constituent functional groups of the solvents on the CO2 affinities as there was no possibility of a glycerol molecule or its derivatives encircling a CO2 molecule sterically. Consequently, the minimum value of the profile of 3-methylpentane, which has no hydroxyl groups, was remarkably larger than those of glycerol and its derivative alcohol molecules. The terminal snapshots for the single CO2 molecule/solvent molecule pairs confirm that the energetic stabilization by steric enclosure was successfully excluded. Therefore, these results strongly suggest that a hydroxyl group in a solvent molecule is a key factor for CO2 affinity. Our predicted free energy profiles also suggest that ether bonds alone do not contribute to the enhancement of the CO2 affinities. Even if ether bonds enhance the affinities, their contributions probably combine with those of other types of functional groups. We conclude that CO2 solubility is determined by both the affinities of the constituent functional groups of a solvent molecule and a steric void effect between a CO2 molecule and a solvent molecule. Furthermore, hydroxyl groups function as strongest promoters of CO2 solubility than ether bonds, methoxy groups, and alkyl groups. Free energy calculations provide a new picture of the significant factors of CO2 solubilities at the atomistic levels.

Figure 9. Snapshots of CO2 approaching a solvent molecule at 107 MD steps in vacuum: (a) glycerol, (b) 1,2-butanediol, (c) 2methylpropane-1,3-diol, (d) 2-methylbutanol, (e) 3-pentanol, and (f) 3-methylpentane; the temperature was set at 298 K. The snapshot for the glycerol molecule (a) was reprinted from our previous study20 with permission. Copyright 2016 Society of Chemical Engineers, Japan.

CO2 Affinity of a Solvent Molecule. The free energy calculations in solvent and vacuum systems provide a new picture of the significant factors affecting CO2 solubilities in conventional EG-based physical solvents at an atomistic level. The CO2 affinity of a solvent is determined by both the constituent functional groups of the solvent molecule and the steric void effect between a CO2 molecule and a solvent molecule. Our work suggests that the free energy profiles can present a thermodynamic assessment in terms of CO2 affinities. Sufficient sampling was performed when estimating the free energy profiles for a CO2 molecule approaching an EG solvent in the vacuum models, as indicated in Figures S1−S5. However, sufficient sampling was not performed for our conventional MD simulations when evaluating the free energy profiles, particularly around the minimum for an EG solvent with a longer chain in the solvent models (shown in Figure 5). More investigations into the solvent models are needed to evaluate the absolute values of the minimum. For example, optimization of the potential parameters should be conducted to achieve a highly accurate prediction of the CO2 affinities. In addition, it is generally difficult to take sufficient statistical samplings for the free energy calculation.32,33 Our next approach will be to perform sufficient sampling by adopting several additional approaches, such as high-temperature configuration-space exploration34 and replica exchange method.35

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CONCLUSIONS In this study, investigation of the detailed mechanisms of physical absorption of CO2 by ethylene-glycol-based solvents at the atomistic levels and free energy profiles of CO2 approaching several types of solvent molecules and their derivatives were evaluated using MD calculations to investigate the effects of the constituent groups of solvent molecules and steric effects in the vicinity of a CO2 molecule on CO2 affinities. We predicted the profiles of a CO2 molecule approaching a solvent molecule in pure component solvent molecules (EG1, EG2, EG3, EG4, DEGDME, and glycerol). The heights of the desolvation barriers in the free energy profiles decreased in the order glycerol > EG1 > EG2 > DEGDME > EG3 > EG4, although more sufficient data samplings should be taken to allow more accurate calculations of profiles particularly around the contact minima. The heights of the desolvation barriers decreased with an increase in the molecular length, except for the profiles of

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b01074. Additional data and free energy profiles (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81-52-735-5214. Fax: +81-52-735-5255. Notes

The authors declare no competing financial interest. F

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ACKNOWLEDGMENTS This work was supported by the education and research infrastructure expenses in Nagoya Institute of Technology. We would like to thank Editage (www.editage.jp) for English language editing.

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DOI: 10.1021/acs.iecr.6b01074 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX